Influence of uniaxial stress on the lamellar spacing of eutectics

Directional solidification of lamellar eutectic structures submitted to uniaxial stress is investigated. In the spirit of an approximation first used by Jackson and Hunt, we calculate the stress tensor for a two-dimensional crystal with triangular surface, using a Fourier expansion of the Airy function. crystal with triangular surface in contact with its melt, given that a uniaxial external stress is applied. The effect of the resulting change in chemical potential is introduced into the standard model for directional solidification of a lamellar eutectic. This calculation is motivated by an observation, made recently [I. Cantat, K. Kassner, C. Misbah, and H. M\"uller-Krumbhaar, Phys. Rev. E, in press] that the thermal gradient produces similar effects as a strong gravitational field in the case of dilute-alloy solidification. Therefore, the coupling between the Grinfeld and the Mullins-Sekerka instabilities becomes strong, as the critical wavelength of the former instability gets reduced to a value close to that of the latter. Analogously, in the case of eutectics, the characteristic length scale of the Grinfeld instability should be reduced to a size not extremely far from typical lamellar spacings. In a Jackson-Hunt like approach we average the undercooling, including the stress term, over a pair of lamellae. Following Jackson and Hunt, we assume the selected wavelength to be determined by the minimum undercooling criterion and compute its shift due to the external stress. we realize the shifting of the wavelength by the application of external stress. In addition, we find that in general the volume fraction of the two solid phases is changed by uniaxial stress. Implications for experiments on eutectics are discussed.Comment: 8 pages RevTex, 6 included ps-figures, accepted for Phys. Rev.

Songs of Scandinavia and northern Europe. A collection of 83 national and popular songs of Russia, Poland, Lithuania, Finland, Sweden, Norway, Denmark, and Holland

Pianoforte acc. --- The Russian national anthem -- At the window -- Stay! oh stay! -- Ah! tell me why -- Tears -- Wanderer's night song -- Peace -- Parting's sorrow -- The Nightingale -- Oh pray! -- Friendship -- The gipsy's song -- Oh! Tell it her -- Forsaken -- The Jamschick's complaint -- The talisman -- The Cossack's lullaby -- The Cossack's song -- The Cossack -- Three-in-hand -- Three-in-hand -- The turtle dove -- Parting sorrow -- The soldier's farewell -- Polish national song -- Mazurek -- Tell me now, my little darling -- Laura to Filon -- Make a bargain, pretty sweetheart -- To the lark -- The bride's farewell -- Finnish rune -- Wilt thou soon return? -- Charles John -- Midst roses sweet -- Courting -- A summer evening -- The sparrow -- On the mountain -- The young postillion -- Old age -- Ah! my sad song dies away -- Disappointed expectation -- Silvio to Laura -- Ever near -- Joy -- Suspicion -- Afar -- A missive unto her I'll send -- No! no more with yearning -- The beggar-boy -- The orphan -- Sorrow's might -- Little Katie -- Come, oh fairest maiden! -- Brave of heart and warriors bold -- To rest I call ye lambkins all -- Abandoned -- Guldterning -- Reindeer song -- King Christian -- The Dannebrog -- Denmark, by whose verdant strand -- Denmark -- A soldier brave -- Fly birdie, fly! -- Little Karen -- The knight's courtship -- Journeyman's song -- By the sea shore -- Farewell, darling Maggie -- Dutch national song -- Flanders -- William of Nassau -- The tithe -- Old Dutch ballad -- The gay fisherboy -- The Greek huntsman -- The patriots -- The merry maidens -- The Flemish maiden and the Frenchman -- A little flower -- The little witch -- My heart's belov'd is mine

The effect of heterogeneity in measles vaccination on population immunity

High overall vaccination levels sometimes hide pockets of poor coverage. We adopted a meta-population framework to model local aggregation of populations, and used this to investigate the effects of vaccination heterogeneity. A recent survey of antibody levels in a community with low vaccination levels in The Netherlands enabled us to assess the relative importance of local and long-range infective contacts, and thus identify feasible levels of aggregation in the meta-population model. In the aggregated model, we found that heterogeneity in vaccination coverage can lead to a much increased rate of infection among unvaccinated individuals, with a simultaneous drop in the average age at infection

Dynamics of the 2001 UK foot and mouth epidemic: stochastic dispersal in a heterogeneous landscape

Foot-and-mouth is one of the world's most economically important livestock diseases. We developed an individual farm-based stochastic model of the current UK epidemic. The fine grain of the epidemiological data reveals the infection dynamics at an unusually high spatiotemporal resolution. We show that the spatial distribution, size, and species composition of farms all influence the observed pattern and regional variability of outbreaks. The other key dynamical component is long-tailed stochastic dispersal of infection, combining frequent local movements with occasional long jumps. We assess the history and possible duration of the epidemic, the performance of control strategies, and general implications for disease dynamics in space and time